db = 23.7 in B C D 96 k bf = 8.97 in tf = in k = 1.09 in 13 Fy = 50 ksi Fu = 65 ksi Member A-B, Interior column: A E

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1 line B1, second floor. t = thickness of connected part Pu = factored load to be resisted d = diameter of the bolt eb = one-half the depth of the beam, in. ec = one-half the depth of the column, in. Hub = factored shear force for gusset-to-beam connection. Vub = factored axial force for gusset-to-beam connection. Huc = factored shear force for gusset-to-column connection. Vuc = factored axial force for gusset-to-column connection. N = horizontal distance of gusset plate, in. V = vertical distance of gusset plate, in. α = distance from the face of the column flange to the centroid of the gusset-to-beam connection, in. β = distance from the face of the beam flange to the centroid of the gusset-to-column connection, in. g = workable gage. rut = tensile force per bolt ruv = shear force per bolt Ft = nominal tensile strength of bolt. D = number of sixteenths-of-an-inch in the fillet weld size. ex = horizontal component of eccentricity of Pu with respect to centroid of weld group. C = coefficient for eccentrically loaded weld groupd C1 = electrode strength coefficient Member A-E, Interior floor girder: Pu = k W24x68 ASTM 992 db = 23.7 in B C D 96 k bf = 8.97 in tf = in k = 1.09 in 13 Fy = 50 ksi Fu = 65 ksi Member A-B, Interior column: A E W10x49 ASTM dc = 9.98 in tw = 0.34 in bf = 10 in tf = 0.56 in 2L6x4x1/2 W10x49 Fy = 50 ksi Fu = 65 ksi 13 Member A-C, : 15 2L6x4x1/2LLBB A36 Ag = 9.5 in 2 Fy = 36 ksi Fu = 58 ksi Gusset plate: α = 16.5 in. β = 6.7 in. t = 1/2 in. N = 20 1/8 in. V = 13 3/4 in. W.P. W24x68 SHEET 125 of 131

2 SHEET 126 of 131 eb = in. ec = 4.99 in. Calculate gusset interface forces: r = ( (α+ec) 2 + (β+eb) 2 ) = 28.4 in. On the gusset-to-column connection: Huc = ec * Pu/r = 22.3 Kips Vuc = β * Pu/r = 30.0 Kips On the gusset-to-beam connection: Hub = α * Pu/r = 73.8 Kips Vub = eb * Pu/r = 53.0 Kips Vu Pu Hu Huc Vuc Hub Vub

3 SHEET 127 of 131 Design of gusset-to-column connection: Try : 2L4x4x5/8 welded to the gusset and bolted with 4 rows of 3/4 in. diameter A325-N bolts in standard holes to the column flange. Use 3 in. spacing between bolts and lev = 1.5 in t = 5/8 Fy = 36 ksi Ab = 0.44 in 2 Fu = 58 ksi n = 8 rut = Huc / n = ruv = Vuc / n = 2.8 Kips/bolt 3.7 Kips/bolt Ft = (fv) < 90 ksi ; Ft = 95.8 ksi > 90 ksi fv = ruv / Ab = 8.48 ksi Ft = 90.0 ksi φ Rn = φ * Ft *Ab = kips/bolt > rut Bearing strength per bolt is: φ Rn = φ (2.4*d*t*Fu) = 48.9 Kips/bolt > φ Rn (table 7-10) = 15.9 Kips/bolt Check prying action : (Illustration of variables in prying action calculations LRFD fig. 9-4) g = 2 in. (LRFD Fig. 10-6) b = g - t/2 = 1.69 in a = (angle leg) - g = 1.50 in < 1.25 b= 2.11 in a = 1.50 in.

4 SHEET 128 of 131 b' = b - d/2 = a' = a + d/2 = 1.31 in in. ρ = b' / a' = 0.7 β = 1/ρ (φrn / rut -1)= if β > 1, α' = 1.0; δ = 1 d'/p = if β < 1, α' = 1/δ (β/(1-β)) 0.63 α' = 1.0 p = 2.0 in t req. = ( (4.44 * rut * b ) / ( p * Fy * (1+ δ * α ))) t req. = in. < 5/8 in. angles are Ok! 2L 4 x 3 1/2 x 1/2 3.5" 1.25" 3" λ 3"

5 SHEET 129 of 131 Design of column-to-gusset connection : Try : 2L4x4x5/8 welded to the gusset and bolted with 4 rows of 3/4 in. diameter A325-N bolts in standard holes to the column flange. Use 3 in. spacing between bolts and lev = 1.5 in W10x49 V β λ Angles 2L6x4x1/ eb ec α N t = 1/2 Fy = 36 ksi Ab = 0.44 in 2 Fu = 58 ksi n = 4 rut = Huc / n = ruv = Vuc / n = 4.0 Kips/bolt 9.2 Kips/bolt Ft = (fv) < 90 ksi ; Ft = 42.3 ksi > 90 ksi fv = ruv / Ab = ksi Ft = 42.3 ksi φ Rn = φ * Ft *Ab = kips/bolt > rut Bearing strength per bolt is: φ (2.4*d*t*Fu) = 39.2 Kips/bolt > φ Rn (table 7-10) = 15.9 Kips/bolt

6 SHEET 130 of 131 Check areas: (since their strengths are the same this will check which section governs in block shear design) Angles Shear areas: Both Angles: (double the area) Agv = in 2 Agv = in 2 Anv = 3.59 in 2 Anv = in 2 Tension areas: Agt = 0.75 in 2 Agt = 1.5 in 2 Ant = 0.53 in 2 Ant = in 2 Shear areas: Agv = in 2 Anv = 3.84 in 2 Tension areas: Agt = 1.00 in 2 Ant = 0.78 in 2 The gusset plate will govern the design because it has less area than the angles. Check Block shear in gusset plate: Shear rupture design strength φvn: LRFD J4-1 φ(.6*fu)*anv = kips Tension rupture design strength φtn: LRFD J4-2 φfu*ant = kips The larger fracture term controls: LRFD J4-1 controls Pu = Vuc = 30 k Block shear strength: φ Rn = kips < φ Rn = kips > Pu = 30 kips

7 SHEET 131 of 131 Design of gusset-to-beam connection: Pub = (Hub 2 + Vub 2 ) = D req = 1.4 Pub / (1.392 *N) = 0 say 2 sixteenths from LRFD table J2.4 the minimum weld size required is : 4 sixteenths gusset plate thickness = 1/2 Use : 4 sixteenths in. fillet welds Check local web yielding of the beam: φ Rn = φ (N k) Fyw * tw = kips > Vub = 53.0 kips (φ = 1) W10x49 t = 1/2" 2L6x4x1/2 Gusset to beam connection 1/4" Fillet welds Gusset to column connection 4 rows of 3/4" bolts W24x68